Multis tiscale cale modelling lling of CMS electric ctrical al - - PowerPoint PPT Presentation

CMS HIP

Multis tiscale cale modelling lling of electric ctrical al breakdown kdown at high h electric ctric field

Flyura Djurabekova, Helga Timkó, Aarne Pohjonen, Stefan Parviainen, Leila Costelle and Kai Nordlund

Helsinki Institute of Physics and Department of Physics University of Helsinki Finland

Flyura Djurabekova, HIP, University of Helsinki

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 Arcing occurs in fusion reactors:

• in regions in direct contact with the plasma such as

the divertor

• in region not in direct contact with the plasma such as

the limiters Arc is a significant source of erosion of first wall material and has even been reported to remove limiter coating layers entirely! Matter flying from the wall into the plasma in an arc can disrupt the normal

• peration

Flyura Djurabekova, HIP, University of Helsinki

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Flyura Djurabekova, HIP, University of Helsinki

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Stage 1: Charge distribut ution n @ surface Metho hod: DFT with externa nal electric field Stage 4: Plasma evolut ution, n, burning of arc Metho hod: Particle-in in-Cell (PIC) Stage 5: Surface damage due to the intens nse ion bombardment ent from plasma Metho hod: Arc MD

~few fs ~few ns ~ sec/hours ~10s ns ~ sec/min ~100s ns

Stage 2: Atomic motion n & evaporation n + + Joul ule heating ng (electron n dynamics) Metho hod: Hybrid ED&MD model (includ udes Laplace e and heat equation solutions) Stage 3b: Evolut ution of surface morpho hology y due to the given charge distribut ution n Method hod: Kinetic Monte e Carlo Stage e 3a: Onset of tip growth; h; Dislocation n mecha hanism Metho hod: MD, Molecular Statics…

• R. Behrisch,

, Plenum, 1986

Flyura Djurabekova, HIP, University of Helsinki

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 In our group we use all main atomic-level simulation

methods:

 Density functional theory (DFT)

 Solving Schrödinger equation to get electronic

structure of atomic system

 Molecular dynamics (MD)

 Simulation of atom motion, classically and by DFT

 Kinetic Monte Carlo (KMC)

 Simulation of atom or defect migration in time

 Simulations of plasma-wall interactions

 Simulation of plasma particle interactions with

surfaces

 We use all of them to tackle the arcing effects!

Flyura Djurabekova, HIP, University of Helsinki

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Macroscopic field to…

   

surface surface

Q E A

…the atomic level:

 



a i C 0i 2 i 0i

q q 1 F r 4 r



L

F Eq

Two electric forces modify the motion

• f charged atoms:

+

Due to the external electr tric field d the surface e attains charge ge

+ a + b +

a

F

b

F

coulomb

F

b

F 

a

F 

+ a + b +

a

F

b

F

coulomb

F

b

F 

a

F 

+ a + b + b +

a

F

b

F

coulomb

F

b

F 

a

F 

 Gauss law by ’pllbox’ technique

0.01 1GV E m  

Flyura Djurabekova, HIP, University of Helsinki

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Solut ution n of 3d Laplace ce equation n for the surfa face ce with h the tip of 20 atomi mic c layer ers, s, mixed ed bounda undary y condit dition n (color represent esents s the charges) es)

2

  

Flyura Djurabekova, HIP, University of Helsinki

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Atom/cluste cluster r evaporat atio ion n from Cu(100) @ 500 K, E0  1 GV/m

Flyura Djurabekova, HIP, University of Helsinki

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 Follow evolution of the

surfaces by calculating the partial charge induced on metal surface atoms

 The dynamics of atom charges

follows the shape of electric field distortion on tips on the surface

 Temperature of the surface

is sufficient, atom evaporation enhanced by the field can supply neutrals to build up the plasma densities above surface.

F.

• F. Djurabek

ekova va, S. Parvi viainen nen, A. Pohjonen nen and K. Nordlund und, , PRE 83, 026704 (2011).

Flyura Djurabekova, HIP, University of Helsinki

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 DFT details:

• Code: SIESTA
• For exchange and correlations

functionals the Perdew, Burke and Ernzerhof scheme of Generalized gradient approximation (GGA)

• Slab organized in 8 layers+ 8

layers of vacuum

• External field is added to calculate

the electrostatic potential in the vacuum

Eo=-1 GV/m

2 2

16 16

5.53 10 5.49 10

surf e e m m surf

Q E A          

Flyura Djurabekova, HIP, University of Helsinki

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 We have calculated the

workfunction for Cu surface when a single adatom is present

F s V

E W E      

WS EV

Flyura Djurabekova, HIP, University of Helsinki

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 Every atomic column produces the current dependent on the field

above the column. The current from the tip is an average over all the columns.

( , , ) ( , , ) ( , )

T

J E T E T J E     

Je

Ei E0

 

2 3/2 0( , )

exp / ( , ) ( , , ) sin / ( , )

B T T B T

aE b J E E k T d E E T k T d E                         

2 2 3/2

A V 1.541 8 eV 8 2 V 6.831 3 eV nm

P P

e a h m b eh       

Fowler- Nordheim constants:

Flyura Djurabekova, HIP, University of Helsinki

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The heat conduction from the tip has been implemented into PARCAS by solving the heat conduction equation Here CV volumetric heat capacity. Phonons are implicitly present in classical MD. In the equation we include

• nly electron thermal conductivity given

by the Wiedemann- Franz law

 

2 2 2

( , ) 1 ( , ) ( , ) ( ) ( )

e V

T x t T x t T x t J x K T t C x             

( ) ( )

e

LT K T T  

2 2 8

• 2

( /3)( ) 2.443 10 W K

B

L k 



   

• S. Parviainen, F. Djurabekova, H. Timko, and K. Nordlund,

Comput

• ut. Mater. Sci. 50, 2075 (2011).

J

el(x)

T, K

J(x)

T, K

Where Lorenz number is found as

Flyura Djurabekova, HIP, University of Helsinki

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 The dislocation motion is strongly bound to the atomic structure

• f metals. In FCC (face-centered cubic) the dislocation are the

most mobile and HCP (hexagonal close-packed) are the hardest for dislocation mobility.

Flyura Djurabekova, HIP, University of Helsinki

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 We simulated a void near

{110} Cu surface , when the high tensile stress is applied

• n the surface. Bottom is

fixed, lateral boundary allowed to move in z direction.

• A. Pohjonen, F. Djurabekova, et al., Dislocation nucleation

from near surface void under static tensile stress on surface in Cu, Jour. Appl. Phys. 110, 023509 (2011).

Flyura Djurabekova, HIP, University of Helsinki

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 Half-void of diameter 4nm in {110} Cu surface. (N of

atoms 170000 atoms…)

 E0=22 GV/m (exaggeration is required to simulate the

dislocation within the MD time span)

 T = 600 K

Flyura Djurabekova, HIP, University of Helsinki

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 A screw dislocation placed so that it

intersects the void on a side, showed a cross-slip behavior leading to the atom step on the

• surface. This mechanism eventually

combines with the previous mechanism, but to ignite this process less stress is required (in

• ur simulations 1.7 GPa against 3

GPa).

Flyura Djurabekova, HIP, University of Helsinki

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 In real life we can observe the full dynamic range of a

vacuum discharge:

• > 10s pA in ‘weak’ FE phase
• Space charge limited ‘strong’ FE phase, typically ~ nA – μA
• Discharge current, up to 10 – 100 A

 At the same time, the involved area changes:

• Typically 10-20 – 10-14 m2 for weak FE  Rem ~ 0.1 – 100 nm
• During the discharge, the bombarded area has R ~ 10 – 100

μm

Up to 12 orders

• f magnitud

ude differenc nce Up to 12 orders

• f magnitud

ude differenc nce

FE FE e

• 10s nm

Discharge ge

e

• 10s μm

Cu Cu+

Flyura Djurabekova, HIP, University of Helsinki

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• H. Timko, K. Matyash, R. Schneider, F. Djurabekova, K. Nordlund,
• A. Hansen, A. Descoeudres, J. Kovermann, A. Grudiev, W.

Wuensch, S. Calatroni, and M. Taborelli , Contrib. Plasma Phys. 51, 5-21 (2011)

Corres espond nding to experi erimen ent... ..

Up Up to to now we we have electros rosta tatic tic PIC PIC-MCC codes: 1d3v the 2D-model

Provide de us with a link betwe ween

• 1. Micro- & macroscopic surface processes: Triggering

(nano-scale)  plasma  crater formation (visible effect)

• 2. Theory & experiments: Using reasonable physical

assumptions (theory), the aim is to predict the evolution of measurable quantities (experiment)

jFE

Flyura Djurabekova, HIP, University of Helsinki

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Flyura Djurabekova, HIP, University of Helsinki

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 Fully cathode dominated phenomenon  Although FE starts from a small area, the discharge

plasma can involve a macroscopic area on the cathode

 Transitions seen:

1.

Transition from strong FE to a small discharge plasma

• Sudden ionisation avalanche
• A plasma sheath forms, the plasma becomes quasi-

neutral

• Focusing effect

2.

Transition from a surface-defined phase to a volume- defined phase

• When neutrals fill the whole system
• Self-maintaining
• Macroscopic damage

1. 2.

0.96 ns 1.06 ns 1.60 ns

Flyura Djurabekova, HIP, University of Helsinki

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Huge fluxes s of accele lerat rated ed ions are the reaso son n for surfac ace damage

Ion fluxes leave rims of peculiar shape

Flyura Djurabekova, HIP, University of Helsinki

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Top left: tilted SEM image (CERN) Top right: tilted AFM (atomic force microscopy) Below: simulation images coloured with respect to the height of surface topography

Flyura Djurabekova, HIP, University of Helsinki

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• H. Timko, F.

Djurab abekova, va, et al. Phys. . Rev. B 81, 184109 (2010)

Flyura Djurabekova, HIP, University of Helsinki

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 We develop a multiscale model, which comprises the

different physical processes (nature and time wise) probable right before, during and after an electrical breakdown event:

• All the parts of the general model are started in parallel. We

start, continue and develop intense activities to cover all possible aspects.

 Most recently our modeling has shown:

• The trigger of the sparks is explained by plasma discharge;
• Plasma is fed from the tips grown under the high electric field
• Tip growth can be explained by the natural relaxation of

stresses inside of material by the dislocation motion

Fundamental physics Beam proc. Sputtering Oxides ceramics Ionic crystals Glass High Tc oxides Polymers Nuclear materials Applications Nanostructures

Flyura Djurabekova, HIP, University of Helsinki

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